A soil sample has a total wet mass of 20 kg and a total volume of 0.01 $m^3$. After being dried in an oven, the dry mass is 16 kg. The specific gravity of the soil solids ($G_s$) is 2.65. Calculate the moisture content ($w$), bulk density ($\rho_{bulk}$), dry density ($\rho_{dry}$), void ratio ($e$), and degree of saturation ($S$). Assume the density of water ($\rho_w$) is $1000 \text{kg / m}^3$.

A perfectly rigid aluminum window frame holds a pane of annealed glass. The original length of the glass pane is exactly $L_0 = 2.000$ m at $20^\circ \text{C}$. The coefficient of thermal expansion for aluminum is $\alpha_{Al} = 23 \times 10^{-6} /^\circ\text{C}$ and for glass is $\alpha_{glass} = 9 \times 10^{-6} /^\circ\text{C}$. If the temperature rises to $50^\circ \text{C}$ and the glass is rigidly restrained by the much stiffer aluminum frame (which forces the glass to expand by the same amount as the aluminum), what is the resulting thermal stress in the glass? Assume the elastic modulus of glass is $E_{glass} = 70$ GPa.

A standard structural steel tension test specimen has an original diameter of $12.5 \text{mm}$ and a gauge length of $50.0 \text{mm}$. A tensile force of $40 \text{kN}$ is applied, and within the elastic range, the gauge length increases by $0.081 \text{mm}$. Calculate the applied stress, the resulting strain, and the Modulus of Elasticity ($E$) of the steel.